Geodesic
The Genuine Omega-regular Unitary Dual of the Metaplectic Group
Canadian journal of mathematics, Tome 64 (2012) no. 3, pp. 669-704

Voir la notice de l'article provenant de la source Cambridge University Press

We classify all genuine unitary representations of the metaplectic group whose infinitesimal character is real and at least as regular as that of the oscillator representation. In a previous paper we exhibited a certain family of representations satisfying these conditions, obtained by cohomological induction from the tensor product of a one-dimensional representation and an oscillator representation. Our main theorem asserts that this family exhausts the genuine omega-regular unitary dual of the metaplectic group.
DOI : 10.4153/CJM-2011-075-x
Mots-clés : 22E46, Metaplectic group, oscillator representation, bottom layer map, cohomological induction, Parthasarathy’s Dirac Operator Inequality, pseudospherical principal series 
Pantano, Alessandra; Paul, Annegret; Salamanca-Riba, Susana A. The Genuine Omega-regular Unitary Dual of the Metaplectic Group. Canadian journal of mathematics, Tome 64 (2012) no. 3, pp. 669-704. doi: 10.4153/CJM-2011-075-x
@article{10_4153_CJM_2011_075_x,
     author = {Pantano, Alessandra and Paul, Annegret and Salamanca-Riba, Susana A.},
     title = {The {Genuine} {Omega-regular} {Unitary} {Dual} of the {Metaplectic} {Group}},
     journal = {Canadian journal of mathematics},
     pages = {669--704},
     year = {2012},
     volume = {64},
     number = {3},
     doi = {10.4153/CJM-2011-075-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-075-x/}
}
TY  - JOUR
AU  - Pantano, Alessandra
AU  - Paul, Annegret
AU  - Salamanca-Riba, Susana A.
TI  - The Genuine Omega-regular Unitary Dual of the Metaplectic Group
JO  - Canadian journal of mathematics
PY  - 2012
SP  - 669
EP  - 704
VL  - 64
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-075-x/
DO  - 10.4153/CJM-2011-075-x
ID  - 10_4153_CJM_2011_075_x
ER  - 
%0 Journal Article
%A Pantano, Alessandra
%A Paul, Annegret
%A Salamanca-Riba, Susana A.
%T The Genuine Omega-regular Unitary Dual of the Metaplectic Group
%J Canadian journal of mathematics
%D 2012
%P 669-704
%V 64
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-075-x/
%R 10.4153/CJM-2011-075-x
%F 10_4153_CJM_2011_075_x

[1] [1] Adams, J., Barbasch, D., Paul, A., Trapa, P., and Vogan, D., Unitary Shimura correspondences for split real groups. J. Amer. Math. Soc. 20(2007), no. 3, 701–751. Google Scholar | DOI

[2] [2] Huang, J.-S., The unitary dual of the universal covering group of GL(n, R). Duke Math. J. 61(1990), no. 3, 705–745. Google Scholar | DOI

[3] [3] Knapp, A. and Vogan, D., Cohomological induction and unitary representations. Princeton Mathematical Series, 45, Princeton University Press, Princeton, NJ, 1995. Google Scholar

[4] [4] Pantano, A., Paul, A., and Salamanca-Riba, S., The omega-regular unitary dual of the metaplectic group of rank 2. In: Council for African American researchers in the mathematical sciences, V, Contemp. Math., 467, American Mathematical Society, Providence, RI, 2008, pp. 1–47. Google Scholar

[5] [5] Pantano, A., Unitary genuine principal series of the metaplectic group. Represent. Theory 14(2010), 201–248. Google Scholar | DOI

[6] [6] Parthasaraty, R., Criteria for the uniterizability of some highest weight modules. Proc. Indian Acad. Sci. Sect. A Math. Sci. 89(1980), no. 1, 1–24. Google Scholar | DOI

[7] [7] Paul, A., Howe correspondence for real unitary groups. J. Funct. Anal. 159(1998), no. 2, 384–431. Google Scholar | DOI

[8] [8] Paul, A., On the Howe correspondence for symplectic-orthogonal dual pairs. J. Funct. Anal. 228(2005), no. 2, 270–310. Google Scholar | DOI

[9] [9] Salamanca-Riba, S., On the unitary dual of some classical Lie groups. Compositio Math. 68(1988), no. 3, 251–303. Google Scholar

[10] [10] Salamanca-Riba, S., On the unitary dual of real reductive Lie groups and the Aq(_)-modules: the strongly regular case. Duke Math. J. 96(1999), no. 3, 521–546. Google Scholar | DOI

[11] [11] Salamanca-Riba, S. and Vogan , D. A..Jr, On the classification of unitary representations of reductive Lie groups. Ann. of Math. 148(1998), no. 3, 1067–1133. Google Scholar | DOI

[12] [12] Vogan , D. A.Jr., Representations of real reductive lie groups. Progress in Mathematics, 15, Birkhäuser, Boston, MA, 1981. Google Scholar

[13] [13] Vogan, D. A. Jr., Unitarizability of certain series of representations. Ann. of Math. 120(1984), no. 1, 141–187. Google Scholar | DOI

[14] [14] Vogan, D. A. Jr., The unitary dual of G2. Invent. Math. 116(1994), no. 1–3, 677–791. http://dx.doi.org/10.1007/BF01231578 Google Scholar

Cité par Sources :